Although the theory of Gabor Analysis, i.e. the decomposition of distributions over locally compact groups in terms of TF-shifted copies of a Gabor atom along a lattice is theoretically well understood there are still many interesting open questions concerning the practical realization of such a program.

Aside from the classical case, where one-dimensional signals on the real line are expanded, using a separable TF-lattice of the form $aZxbZ$ there is no easily applicable and computationally realizable approach to the actual determination of Gabor coefficients for more general lattices, or for multi-dimensional signals.

The talk will address computational issues, the theoretical justification of numerical approximations to the continuous problem, and mention a list of open problems in the field which would be relevant for further progress and real-world applications of Gabor analysis. We will also discuss aspects of the question, what makes a Gabor frame a good one.